JGV 1281 
.R65 

Copy 1 



THE 








and 



OTHER AXIOMS 



of 



Bridge Whist 



EDMUND ROBERTSON. 



Price per single copy — 10 cents 
Fifty copies —4 dollars. 



NEW YORK 

Pl'DBfi of "Bollettino dellft *ei;t'. 
ITS Park Bow, 

1903, 



THE 



ROBERTSON RULE 

and 

OTHER AXIOMS 

of 

Bridge Whist 

by 
EDMUND ROBERTSON. 



Price per single copy — 10 cents 
Fifty copies — 4 dollars. 



NEW YORK 

Fress of "Bollettino della Sera", 
178 Park Row. 

100%. 



THE LIBRARY OF 
CONGRESS, 

Two Comta Receives 

OCT, if 1902 

CoPVBIOMT ENTRY 

CLASS ft-XXo, Wo, 

uzG(o c f 



Copyright 1902, 
By Edmund Robertson. 



THE ROBERTSON RULE. 

It is now pretty generally recognised that, in or- 
der to take full advantage of the deal/the chances that 
the expensive declarations present for making game 
should be first examined. 

Seeing that the value of each trick is highest in 
no trumps and that it is the shortest road to game, 
the dealer's first thought on looking at his hand 
should be: "Am I strong enough to go no trumps?" 

Before considering the measure of strength on 
which it would be sound to call no trumps it is ne- 
cessary to remember that the dealer has two impor- 
tant advantages. The first is the right to select the 
trump suit and the second is a knowledge of the cards 
he can depend upon to take tricks when Dummy's hand 
is placed on the table. 

The enormous advantage of knowing what cards 
are in his favor, where .finesses are praticable, and 
what suits have a chance of being established is alone 
sufficient to ensure the odd trick in no trumps with 
all round average hands — because the dealer not 
only sees but commands two hands. 

But this is not by itself a sufficient reason for 
calling no trumps with only an average hand. The 
odd trick in your deal is of. more value to the adver- 
saries than to yourself, because if they manage to score 
in your deal they will probably make game when it 
is their turn to declare trumps. If there is any doubt 
about the odd trick always make it a principle to pre- 
vent the adversaries from reaching one o-f the "useful" 
stages when they have the deal to go on with. 

It is therefore not sound to declare no trumps 
unless your hand contains at least one probable trick 
above the average, i, e., unless you are more or less 
certain of the odd trick and hope to score two by 
cards. 



There is another point to be considered. The lead 
being with the adversaries, if you are not protected 
in the majority of the suits, i. e., three (out of the four) 
it may happen that each of your opponents has a long 
suit and you may not get the lead in time to save the 
game. 

The general principle therefore on which it would 
be sound ti declare no trumps is that your hand 
should contain one very probable trick above the ave- 
rage with three suits protected. A suit is not absolutely 
protected in "no trumps", unless it contains one of the 
following combinations : 



Ace 



King 


King 


King 


Qn. 


Qn. 


Jack 


7 


io 


Qn. 


IO 


Jack 


IO 


6 


3 




6 


3 


3 


5 






3 




2 



X 



Theoretically an average hand contains 3%. tricks 
Your hand taken with your partner's will on the ave- 
rage take 6y 2 tricks. If your hand contains one very 
probable trick above the average your combined hands 
will take at least seven tricks, i. e., you have a right 
to expect the odd trick, and may score two by cards. 

It becomes therefore very important to know what 
is an. average hand. There are four aces, kings, queens, 
&c, and the hand that contains an ace, a king, a queen,, 
a jack and a ten, i. e., a card of each denomination,, 
may be regarded as a typical average hand. But this 
arrangement is not usual. A hand may contain no ace 
or king and yet be of average strength. 

Without a measure of value it is very difficult, in 
the case of a mixed hand, to know whether it is above 
or below average strength. The following scale of 
values, known ar the "Robertson Rule", may be laid 
down for the purpose of calculating very nearly the 
exact strength of any hand : — 

ACE . . . . equal 

equal 



KING 
OUEEN 
JACK 
TEN 



equal 
equal 
equal 



to 

to 
to 
to 
to 



Total of an an average hand equal to 18 



;--,-■> r -i8 may therefore be regarded as the standard- of 
value of, an average hand. The value (5) assigned, to) 
the : King as compared, with the other Bridge honors- 
is a fraction too much, and those of the Queen, Jack, 
and Ten, too little, but these differences are quite in- 
appreciable in actual play, and may be safely disre- 
garded. It should be remembered that this scale of 
values is mainly intended tor the purpose* of- calculat- 
ing: the strength of a hand with a view to declaring 
no trumps and is based on the mathematical laws 
of chance. 

For the benefit of vacillators we will discuss this* 
valuation at some length. The beginner need not 
puzzle over the next six paragraphs. 

Every card has a threefold value : — 

(1) Its aggressive or trick-taking value. 

(2) Its obstructive value i. e., its power to prevent 
one or more adverse tricks. 

(3) Its protective value, i. e., its power to help 
other friendly cards to take tricks. 

What is the aggressive or trick-taking value of 
say, a guarded king in your hand without the ace of 
the same suit? There are three hands in one of which 
the ace must be, i. e., your partner has one chance out 
of three of holding the ace. Again, if your king is guard- 
ed (say you have K:ing,io,3) it should make a trick if the 
ace is held by the adversary ' to your right, i. e., there 
are two chances out of three that your king will make 
a trick. Assuming the trick-taking value of the ace 
at 1, the abstract trick-taking" value of the king is, 
therefore, in average positions, assuming that it is 
guarded, two out of three. 

The trick-taking value of the queen, jack and ten 
may be deduced in like manner. In average positions, 
assuming that it is guarded, the queen has four 
chances out of nine, the jack eight out of 27, and the 
ten 16 out of 8.1 of taking a trick. Reckoning the value 
(32-243) of the second Dutch honor, the nine, 
would seriously complicate matters, but it is a card 
by no means to be despised in no trumps. 







The value of a card, in so far as its power to 
prevent an adverse trick and its power to help friendly 
forces are concerned, is modified by so many circum- 
stances of position and play that it would be idle to 
lay down an exact scale of values. But in average 
positions the obstructive and protective values of the 

cards in a gradually descending scale from the ace 
downwards are relatively: — 

Ace ... ... ... . . . 81 



King 
Queen 
jack 
Ten 



54 
36 
24 
16 



Similarly the trick-taking worth of a card largely 
depends on what is termed the fall of the cards. In 
average position, however, the abstract threefold rela- 
tive values of the cards are very approximately : — 



Ace 

King 
Queen 
Jack 
Ten 



equal to 81 
equal to 54 
equal to 36 
equal to 24 
, eqal to 16 



A possible objection to this scale of values is that 
only Bridge honors are taken into account, whereas 

small cards also score tricks. When a small card scores 
a trick (especially in no trumps) it can be proved 
to be due to the protective or obstructive value of one 

or more of the Bridge honors. Remember that this scale 
is mainly intended for the purpose of estimating the 
strength of a hand with a view to calling no trumps. 
There is no question in "no trumps" of a two of trumps 
ruffing an adverse ace. What you want to know is 
"How much above the average is my hand?" This 
scale will make the answer easy. 

Let us repeat the Robertson Rule for estimating 
an average hand : — 



ACE 
KING 
QUEEN 
JACK 
TEN > 



equal to 7 
equal to 5 
equal to 3 
equal to 2 
equal to 1 



Average hand' equal to 18 

Having - determined that the standard value of an 
average hand' is 18, the conclusion we arrive at is that 
with one ace (18 plus 7 equals 25) king (18 plus 5 equals 
23) or queen (18 plus 3 equals 21) above average 
strength, i. e., with 21 points or over, and with three 
suits protected, it would be sound to declare no trumps. 
Remember that 21 points is the minimum strength on 
which it would be sound with the score at love all (the. 
score must always be considered) to declare no 
trumps, and three suits must be protected. 

This scale of values should not be applied to a 
Singleton Ace or King or an unguarded Queen, Jack 
or Ten. But every honor in a guarded suit must t>e 
given its full value. 

A Singleton ace, although a certain protection in 
one suit and a consideration as regards the honor 
value of the hand,loses virtue enormously in no trumps 
and should be reckoned at 4 only. Similarly Singleton 
King should be reckoned at 2 only (if your partner 
has not the ace it will force an adverse ace) and an 
unguarded queen at 1. 

SINGLETON ACE ... :.. equal to 4 

SINGLETON KING . . . equal to 2 

UNGUARDED QUEEN . . . equal to 1 

An unguarded JACK or TEN need not be taken into 
account. 

The advantages of a measure of value for deter- 
mining a no trumps hand are enormous. Let us apply 
the test to the following, accepted no trumps hands. 



8 



Hearts 

- , ' i ' * 
Diamonds 

Clubs 

Spade-s 



A95- 7 

Q.J 8.3 5 ; 

^ ! 6. ' ; l 
a.k:7.2 12 

25 



K.Q.7.2 


8 


A.8.7. ; 


.7. 


9.8. . 




A Q 6.5 


10 




25 



K.Q.9.1. 8 
Aid 8. 8 
A.J.65.4.9 

10 

• ; 25 



Hearts 


A.K6.2. 12 


8.5. 


IC9 8 75. 5 


Diatnands 


6 , 


E.QJ.S 10 


A.K4. 12 


Clubs 


A.Q8.4, 10 


, A.10.3. 8 


Q. | 


Spades 


3f.ro 9 T- 3 


A. 9.7.2. 7 


A.6.5.4. 7 




25 


2a 


25 



It will be noticed that these hands come, up to 25, 
i. e., seven points (an ace) above average strength, 18. 
They may be regarded as specimens of fine "no trum- 
pers." With two aces :;: there is always a probability" — ■ 
two chances out of three — of scoring 30 above the line, 



* To tail of into refinements: — 
Ace with one other ... 

King .".". 

Queen 
Jack ... ... 

In practice it is only necessary to remember that 
every honor in a guarded suit of not less that .three 
cams should be given its full value. 



equal to 6 

equal to 4 

equal to 2 

equal to 1 



9 

which is about one-third of the rubber bonus ioo. 

Hands containing two aces, hot singletons or dou- 
l>letons,"and' a third suits absolutely guarded usually 
make the soundest no trumpers if they total up to 21 
•tr over and there is no decided strength in a red suit. 
As we shall! see later, a hand well above average 
strength is not necessarily a u no trumper". There may 
foe^both more profit and more safety in a red trump 
^declaration. 

With four aces (7 multiplied by 4 equals 28) there 
can be no doubt about the declaration. With three* 
aces (7 multiplied by .3 equals 21) unless there is 
sufficient strength in red suit to score game or a very 
large honor score the hand should as a rule be played 
without trumps. Besides the honor score (30) and 
three certain tricks, the protective and obstructive 
value of the aces are so great that the hand may be 
regarded as one very probable trick above average 
strength. : 

The value 7 assigned to the ace does not represent 
its trick-taking value alone, but its combined three- 
fold value. 

It may at first sight appear that as an ace, king, 
queen held in the same hand are equally valuable in 
no trumps they should be reckoned at 7 each. As 
however the protective value of the aces converts the 
king into certain trick and the combined protective 
values of the ace and and king help the queen to take 
a trick, their true values are 7, 5 and 3 respectively. 



*The honor value of: — 

2 Aces ... ... ... equal to 2 

3 " ... ... ... equal to 1 



10 



Other hands generally considered good enough for 
no trumps with the score love all: 



Hearts 


' A.10.8.2. 8 


A.Q.2. 10 


7 6. 


Diamonds 


Q:X6. 5 


J.10.7.3. 3 


J.10 8 2! 3 


Clubs 


K.Q3.2. 8 


Q.8 5/ 3 


Q J. 19- 3. 6 


Spades 


10 5. 


K.6.4. 5 


A.K5. 12 




21 


■ . , 21 


■v- 21 



Hearts 


A.Q8.7. 


9 


A.7.6 ' 7 


K10.3.2. 


7 


Diamonds 


K.10.9. 


6 


K J 0.8.2. 6 


7.4 


, ' . .i. 



Clubs 


QJ.10. 


6 


K.Q.9.3. 8 


A.10.8. 


■8 


Spades 


543 





5.4. 


KJ9.6- 


7 






21 


21 


■ 


21 



Remove even the lowest honor, the ten, from any- 
one of these hands and it will no longer be good 
enough for no trumps, as it will fall below the standard 
no trumper 21. These hands contain only a single ace 
each and are the minimum strength on which you 
should risk no trumps. 

Without an ace it is very seldom sound to go no- 
trumps. Besides a remote possibility of four aces 
being in one hand against the dealer, there is a pro- 
bability of losing 30 for honors. At love all or with 
the score in your favor no trumps should not be de- 
clared unless the hand totals up to. 25. But when only 
the odd trick is needed to score game or when the 
adversaries' score is so far advanced that onlv a bold 



II 

no trumper will save the game or rubber, the risk of 
an adverse honor score may be accepted, with a hand 
that totals up to at least 21. 

Hearts K. J. 9. 8. .. . , . : *■!.. %' 

Diamonds Q. J. 7 " . ... — 5', 

Clubs K. Q. 8 ... ~ ■-..'■;■ ... . 8; 

Spades K..J. 9 .... - .... 7/ 

"• -.'■•■ :,-,.. "■ . .. . .'•,;.'. .■•.-...' >i*f'4%: ' 

This fine hand is 'fully -asking -.and. a queen:, above 
average ^strength and' comes: up to 27. It is a soundl 
no trumper at almost any point of the score. The other 
three hands must hold j f6ur aces, a king, two queens* 
a .jack and four. tens, or a total of 45 points. The pro- 
babilities r are that' Dummy 'will hold his fair share of 
the good cards not in* your .hand', i. e., 45 1 3 equals 15^ 
This 15 and your 27 come up to 42. Playing on the 
probabilities these two hands are as much' superior in? 
trick-taking power tot. the adversaries' as' 42 is to 30 
.(4 13). A superiority' of 7 to 6 is ail that is necessary 
to score the odd trick and owing to the dealer's advari-^ 
tages two by cards is more than probable- — with a fair 
prospect of game. As already pointed out, besides a. 
possibility of four aces being in one hand against you? 
there is a likelihood of losing 30 for honors, but there 
is at least an equal change of scoring 24 for tricks if 
not the game. In all doubtful cases the state of the 
score must decide the declaration. 

It should be noted that 21 is the minimum strength 
on which no trumps should be called with the score 
love all- — this minimum being increased or decreased 
according to the state of the score. When the score 
is decidedly in your favor, i. e., you are 24 or over,. 
unless you hold a fairly unbeatable no trumper (24 or 
over) you shoula search your hand to see whether yon 
have not a reasonable prospect of scoring game on a 
safer and less expensive declaration. But with the 
score dangerously against you an average hand or two 
five cards suits with two aces, or a six card suit 
headed by Ace, King, Queen, are good enough to risk: 
no trumps on. 



12 

II. 

A SYNOPSIS OF BRIDGE 

■ . •• i j 



- ..- 



"..:■':-, DECLARATIONS 



. ;! o , ,., .— )o(— 

An attempt is made in this synopsis to cover the 
'whole - field 5 of the declarations, by laying down: — 

(i) A standard minimum of strength on which 
certain ■■offensive declarations should be made origi- 
nally and on a pass. 

, (2) Arrstandard minimum, of weakness on which 
^defensive declaration should be made originally. 

When once the beginner knows exactly what to 
declare at love all, be will soon be able to make his 
declaration fit the varying conditions of the score. 

The formulas given for no trumps, hearts and dia- 
monds are based on the mathematical laws of chance. 
They may at first sight appear to be too confusing 
to be applied in practice at the card table. Most hands. 
•however, do not admit of an alternative declaration, 
so that in practice it is only necessary to be acquainted 
with the Robertson Rule. In a percentage of hands, 
however, there usually exists a choice between two 
suits, or it may be a choice between two or more suits 
and a pass. In such cases it is clearly important to 
indicate the correct declaration. 

'Generally speaking., when there is a choice be- 
tween no trumps and hearts thes latter should be 
selected, because it is an equally attacking declaration 
and as a rule very much the safer of the two. 

By equally attacking declaration is meant one 
that offers the same chance of game as a no trumper. 
At any point 01 the score only one trick more is needed 
with hearts as trumps to score game. This extra trick, if 
at cannot "be made by utilising one of Dummy's little 
trumps, may as a rule be secured by bringing in a long 
•card owing to the superior powers of re-entry that a 
long trump suit affords. 

When, there is a choice between no trumps and 
diamonds the Jailer, although it may be the safer of 



13 

the two declarations* falls ' away entirely from the 
attacking spirit of the deal, and should not, except 
when the dealer is. playing to the cScoreior /to the state 
of the rubber, be selected in preference to no trumps. 
The objects kept in view in makings out these formu- 
las are. — 

I. To enable a player to know what to declare at 
love , all, by ; laying down a standard^ minimum of 
strength on which certain declarations should be made 
originally and on a pass. , , * >• 

->; -:■■■:%*. -r~ -To show the advantages of a hearts declara- 
tion when there is a choice between hearts-andyno 
trumps. V- ■;.- -;. :•;-" 

3. To point out the disadvantages of a. diamonds 
declaration when there is a choice -between diamonds 
and no trumps. ; i,, 

4. To show the dealer exactly when to use the 
spade shield. . , ..,.,''.':■■ 

5. To correct the tendency of modern Bridge to 
shoulder Dummy with the responsibility of the de- 
claration. .-...•* 

OFFENSIVE DECLARATIONS BY THE 
DEALER AT LOVE ALL 

7 ' NO TRUMPS. 

The dealer should declare no trumps if he has 
three suits guarded and his hand comes up to 21 or 
more, gauged by the Robertson Rule : 

Ace equal to 7. 

King equal to 5. ; f\ 

Queen equal to 3. 

Tack equal to 2. 

Ten equal to 1. % 

Singleton ace equal to 4. 

Unguarded king equal to 2. < 

Unguarded queen equal to 1. '■ 

The minimum for a no trumps declaration is 21 
with three suits guarded. 

At love all or with the score in the dealer's favor 



14 

he should not declare no trumps without an ace 
unless his hand totals up to at least 25. As there are 
a large number of hands not 'guarded' in three 'suits 
which are quite' good enough for "no trumps", the 
dealer should see whether his- hand comes under 

The Seven Rule, which is that the dealer should 
declare no trumps 

With four tricks, and three suits guarded.,, 
'.. Five tricks and two suits guarded. 

Six tricks and one suit guarded. ■■•»;■ 

The declaration will, in fact, be theoretically corn 
rect if the number of tricks in hand plus. the number 
of suits guarded come up to seven or more. • ■ ■ .• - 

A five trick hand, two suits guarded, should'be* 
regarded as a strong attacking hand, and unless he has 
decided strength in a red suit, wich would certainly 
be the safer declaration, the dealer should unhesitat- 
ingly play without trumps. With six or more spades 
to the quint or quart major, even with three suits ab- 
solutely unprotected, the dealer at love all or with' the 
score against him should also declare "no trumps". 
A long solid suit of six or more cards gives the dealer 
a preponderating advantage in playing without 
trumps, and offers a chance of game that should not 
lightly be missed. 

It is a great mistake to suppose that every strong 
hand should be played without trumps. If the dealer's 
hand comes to 21 or more by the Robertson Rule and 
he also holds good hearts, there may be both more 
profit and more safetv in declaring hearts. A sound 
hearts declaration is the best of all possibile makes. 

HEARTS. 

The dealer should declare hearts if his hand totals 
up to 18 or more calculated dv this formula : 
Ace of hearts equal to 7. 
King of hearts equal to 5. 
Queen, Jack and 10 equal to 3 each. 
Every other heart equal to 2. 



15 

Every other* trick equal to 4. 
Every other probable trick equal to 2. 
For 3 honors add 4. 
For 4 honors add 16. 

This formula will enable the dealer to calculate 
the exact value of any hand with hearts as trumps. 
Should he, however, obtain a bigger result by calcu- 
lating the hand according to the Robertson Rule, he 
should of course declare no trumps and, vice versa. .. 

The formula may at first sight appear to be too 
confusing to be applied in actual practice at the card 
table This is not really so, because the ace, king and 
queen of hearts have the same values assigned to them 
as. in the Robertson Rule. All that the player need 
remember is that every heart, other than an honor, 
counts 2; every certain trick 4, and every probable 
trick 2. The value of three or more honors in hearts, 
is self-evident. Such hands hardly need the formula 
to be applied to them. So also with six or more hearts, 
hearts is with very rare exceptions the correct de- 
claration. The formula will, in fact, be only useful 
in cases of doubt between hearts and no trumps when 
the hand contains not more than five hearts. Such 
hands guarded in three suits are the only ones likely 
to admit of an alternative declaration. 

The minimum for a hearts declaration is 18. The 
dealer should not pass the declaration to Dummy if his 
hand comes up to this minimum. 

A detailed explanation of how this formula has 
been arrived at, together with a somewhat more ela- 
borate formula to ensure greater accuracy, will be 



* i. e., for every nearly certain trick, other than 
in the trump suit, such as an ace king or queen, add 
4, and for every probable trick such as a guarded king 
or queen, jack, ten, other than in the trump suit, add 2. 
This formula is not intended to be applied to a hand 
containing only three hearts. When it is applied, to a 
hand containing only four hearts nothing should be 
added for three honors or less. 



She 

found in the Higher Grammar of Bridge,. It would 
be comparatively simple to lay down a formula for 
calculating the trick value of any hand and to show 
the different trick values of the same hand in the dif- 
ferent declarations. Unfortunately the honor-values of 
a "hearts", a "diamonds" and even a "clubs" hand and 
the aces in no trumps are disturbing elements which, 
completely destroy the simplicity of the calculation. 

The beginner need not puzzle over the explana- 
tion that follows. The face value of each trick in hearts 
as compared with "no trumps" is as 8 is to 12. But 
as four tricks, are wanted to score game from love 
all in hearts against three tricks in no. trumps 
the relative values are seemingly as 3 is to 4. But 
these values are further disturbed by the fact that in 
average positions with five or more cards of a suit the 
hand will score one trick more in a trump suit declara- 
tion than if played without trumps. This is usually 
the case with five hearts and almost invariably the 
case with six. So far therefore as scoring game in the 
deal goes, a hearts declaration if sound offers the same 
chance of making game, besides being the safer de- 
claration of the two. 

Taking all these facts into consideration in reckon- 
ing the value of the ace of hearts in no trumps and 
with hearts as trumps, the relative values are ap- 
proximately as 7 is to 6]/ 2 . Moreover the ace of hearts 
is an absolutely certain trick with hearts as trumps. It 
is not so in the dealer's or Dummy's hand in no 
trumps. In actual play such a fraction as 1 1 14 (the dif 
ference between 7 and 6 l / 2 divided by 7) 
is a negligible quantity. For this reason and for the 
sake of uniformity the value of the ace of hearts has 
been set down at 7. The honor value of the ace of 
hearts in either declaration is about the same. 

The trick taking relative value of the king of 
hearts, if deduced in like manner, will be approximate- 
ly 4. But the king of hearts, with hearts as trumps, 
has an honor value which it does not possess in play- 
ing without trumps. The honor values of the ace, king, 
queen, jack and ten are fully one each. The 
full value of the king therefore is approximately five. 



it 

Tfye queen, jack and ten possess an honor value of one 
each, plus their trick taking values which are de- 
pendent on their forming part of the trump suit. 

It would be sufficient, therefore for the purpose to 
ascertain the average trick value of any heart with 
hearts as trumps as compared with the value 7 (see 
the Robertson Rule) of a trick in no trumps. Takings 
7 as the standard value of a trick in no trumps any 
fractional value less than half is quite inappreciable 
in actual play in any declaration. It is clear that the 
value of each heart will depend on the length of the 
suit. With five trumps in average positions after three 
rounds, the dealer will be left with two long trumps,, 
with six he will be left with three. Each heart may 
therefore be reckoned as a probable trick. According 
to the length of the suit their value would range 
between 2 and 3. With five only the value of each 
heart would be approximately 2, with six or more the 
value of each heart would be approximately 3. 

It is clear that in ruffing, in affording protection 
to other friendly cards, in helping to establish the 
dealer's or Dummy's suits, the longer the trump suit 
the greater the value of each individual trump. 

Ace of hearts equal to 7. 

King of hearts equal to 5. 

Queen, jack, and ten equal to 3 ecah. 

Every other heart equal to 2 or 3 according to the 

number of trumps in hand. 

In reckoning the value of each nearly certain and 
each probable trick outside the trump suit,it is tolera- 
bly clear that they lose value by being made in hearts 
at 8 points each instead of of in no trumps at 12 points 
each. This is especially so with aces. In reckoning 
the value of, say the ace of clubs with hearts as trumps 
i}/\ multiplied by 7 equals 21-4) it should be borne in 
mind that it has a distinct honor value in no trumps 
which it does not possess with hearts as trumps. At 
a liberal estimate, therefore, the value of each ace out- 
side the trump suit in a hearts declaration (% multi- 
plied by 7 minus 1) amounts to 4. Similarly the value 
of each probable trick outside the trump suit is 2. 



18 

Every nearly certain trick outside the trump suit 
is equal to 4. . • ■ 

Every probable trick outside the trump suit is 
•equal to 2. 

Owing- to the different honor scores for simple 
honors, double honors, and for four or more held in 
the same hand, it is obvious that a hand containing 
iliree honors (which mean 5 16 certain above the line 
and a probable 32) and a hand containing four ho- 
nors (64 above the line or about two-thirds the rubber 
^bonus 100) have an increased value, which needs to 
Ibe separately taken into account. For 3 honors add 4, 
for 4 honors add 16.. 

DIAMONDS. 

Except with overwhelming strength, many for- 
ward players exclude diamonds aitogether from the 
list of original offensive declarations with the score 
love all, as this call offers a poor chance of game on 
the deal. This conservatism would be sound if the 
•average number of deals in a rubber were 3 or 4 or 
even 5. But experience has shewn that the average 
number of deals in a rubber is seven and a fraction, 
and that Dummy's chances of making a defensive de- 
claration on a pass are about 50 per cent. 

If imable to declare no trumps or hearts the dealer 
should see whether his hand comes up to the minimum 
IS for a diamonds declaration according to the follow- 
ing formula * : — 

Ace of diamonds 4. 

King of diamonds 3. 

Every other diamond 2. 

Every nearly certain trick outside the trump suit 3. 

Every probable trick outside the trump suit 1. 

Fot 3 honors add 3, for 4 honors add 12. 

A weak diamonds declarations, except to the score, 
is a very bad make. 

If the hand gives a bigger result when calculated 
by the Robertson Rule the dealer should unhestitat- 



*This formula is not intended for a hand that 
contains only four diamonds not all honors. 



19 

ingly declare no trumps. He should not pass the de- 
claration if his hand comes up to the minimum 15. 

CLUBS. 

An offensive clubs declaration should as a rule 
only be made to the score. With clubs however to 
four honors other than-A.K. Q.J. ten or A. K.Q. ten 
the dealer should declare clubs when he cannot see his 
way to making a more paying declaration, or is blank 
in the order suits. With ace, queen, jack, 10: or ace, 
king, jack, ten, or king, queen jack, ten and nothing 
else in the other suits, the dealer should declare clubs 
rather than pass the declaration, because the honor 
score, plus the probable trick score, will be found to 
be fully equal to the average value of a deal. In all 
other cases he should leave it to Dummy. 

• SPADES 

An offensive spades declaration except to the 
score is an absurdity. 

Defensive declarations by the dealer. 

THE SPADE SHIELD. 

When the dealers hand totals up to six or less by the 
Robertson Rule he should declare spades. This is an 
irreducible minimum, and should be regarded as the 
standard minimum of weakkness for an original defen- 
sive declaration. 

Without a winning c?rd in his hand the dealer 
should invariably declare spades unless he holds five 
clubs to two honors, or any six cards suit headed by 
an honor. With a six cards suit and nothing else in th^ 
hand it is clear that the hand is utterlv valueless unles^ 
the six cards suit be declared trumps. As a measur 
of protection, therefore, the dealer may be compelle 
to call hearts, with a hand like this : 

Heart: Jack, 9, 8, 7, 5, 4. Diamonds: 8, 4, 2. Club , 
Jack 9, 3. Spade : 8. 



20 



A DEFENSIVE CLUBS DECLARATION 
BY THE DEALER. 

The one exception to the above rule is when the 
dealer holds king, queen, jack and ten of clubs and not 
another remotely probable trick or any six cards suit. 
Clubs should then be declared defensively as well as 
for the sake of the honor score thirtytwo. 

PASSING THE DECLARATION. 

There is too great a tendency in modern Bridge to 
shoulder Dummy with the responsibility of the decla- 
ration With a four trick hand the dealer should make 
the most paying declaration he can — no trumps if pos- 
sible. As a rule, however, at love all with less strength 
than the minimum 21 for no trumps (see also the Seven 
Rule), 18 for nearts, 15 for diamonds, or d honors, in 
clubs, as seen above, he should pass the declaration to 
Dummy, but only if he holds one trick or a hand 
that totals up to at least 7 according to the Robertson 
Rule. As we have already seen, with less than this 
strength the dealer should make a protective declara- 
tion. At love all 7 should be regarded as an irreducible 
minimum for passing the declaration. 

OFFENSIVE DECLARATION BY DUMMY. 

At love all Dummy should declare : — 

No trumps if his hand comes to 22 by the Robert- 
son Rule. 

Hearts 18 (see the hearts formula) ; 

Diamonds 15 (see the diamonds formula). 
When an alternative declaration is open to Dummy 
he should calculate the hand by the Robertson Rule 
and the two formulas stated above, and make the de- 
claration that gives the biggest result. The Seven 
Rule should be worked with extreme caution on a pass. 
If Dummy holds a five trick hand, two suits guarded, 
he should not declare no trumps unless one of the 



21 

guarded suits is red. If both the guarded suits are 
red and neither of them sufficiently long to be mad- 
trumps Dummy should play without trumps. With 
only one long established suit, however, the long suit 
should usually be made trump. 

SPADES 

With less than the minimum strength, 22 for no 
trumps, 18 for hearts and 15 for diamonds, Dummy 
should have little hesitation in declaring spades, unless 
he holds at least six cards in another suit. Clubs 
should not be selected in preference to spades unless 
Dummy holds: 4 to 3 honors (when weak in spades), 
5 to 2 honors, or 6 to 1 honor. 

The attempt to score off a poor hand marks the 
poor player. 



LIBRARY OF CONGRESS 



020 237 428 1 



. a pass. 

.^'guarded, 

one of ill e 



